This invention relates to a tire having an electrically non-conductive tread which contains an electrically conductive rubber strip which extends through at least a portion of the tread to its running surface in a wave configured shape, and therefore not a continuous straight line within said tread, in which at least a portion of the rubber strip is in a shape of, for example, a substantially sinusoidal, cycloidal and/or zigzag form, to thereby provide a mechanical self-locking configuration between tread segments through which the rubber strip extends and divides. In particular, said tread is composed of a cap/base configuration. The outer cap layer is of a relatively electrically non-conductive rubber composition having a running surface intended to be ground-contacting. The tread base layer, underlying the tread cap layer, is of a relatively electrically conductive rubber composition and is not normally intended to be ground-contacting. A thin rubber strip, unitary with and as an extension of said tread base layer, which is thereby relatively electrically conductive, extends radially outward from said tread base layer of which at least a portion of the rubber strip is in a form of a wave-shaped configuration through, and therefore within, said tread cap layer to an outer running surface of said tread cap layer. In practice therefore, said rubber strip extends from, and as a part of, said tread base layer through said tread cap layer. In practice, said thin layer extending in said tread cap exhibits substantially at least one half an undulation, and preferably substantially at least two undulations of its wave configured shape of, for example, a substantially sinusoidal, cycloid al and/or zigzag form. The form of the individual undulations of the wave shaped configuration of the strip within the tread may be the same or different.